A source of sound (1140Hz) emits uniformly in all directions. An observer 3.09m from the source measures a sound level of 38.2dB. Calculate the average power output of the source.
To calculate the average power output of the source, we need to use the concept of sound intensity and the formula for sound intensity in decibels.
Sound intensity is defined as the power of the sound wave per unit area. It is given by the formula:
I = P / A
where I is the sound intensity, P is the power of the sound wave, and A is the area through which the sound wave is passing.
In this case, we need to calculate the power P.
First, let's convert the sound level from decibels to sound intensity using the formula:
I2 = I1 * 10^(L2/10)
where I1 is the initial sound intensity, L2 is the sound level in decibels, and I2 is the final sound intensity.
In this case, the initial sound intensity I1 is unknown, the sound level L2 is 38.2 dB, and the final sound intensity I2 is unknown.
I2 = 10^(L2/10) = 10^(38.2/10) = 10^(3.82) = 6732.57
Now, we can calculate the power P using the formula:
P = I * A
where I is the sound intensity and A is the surface area of a sphere with radius 3.09 m.
The surface area of a sphere is given by the formula:
A = 4 * π * r^2
where r is the radius of the sphere.
A = 4 * π * (3.09)^2 = 119.49 m^2
Now, we can calculate the power P:
P = I * A = 6732.57 * 119.49 = 803676.25 W
Therefore, the average power output of the source is approximately 803,676.25 watts.